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Exam schedule
Winter-Semester 25/26
- Exam: 12.09.2025
Curve Sketching and Optimization Problems
Relevant Exercises (Rhyn): Chapter 3, Section a) Exercises 18, 19, 20, 21, Section b) Exercises 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, Section c) Exercises 40, 41, 42, 43, 44, Section d) Exercises 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71; Chapter 5, Section d) Exercises 44, 45, 46, 47, 48, 49, 50, 51, 51, 52, 53, 54, 56, 57, 58.
Learning Goals:
Be able to determine stationary points using the first derivative.
Be able to apply the concept of the second derivative geometrically to describe curvature behavior.
Be able to calculate inflection points using the second derivative.
Be able to determine the type of a stationary point using the second derivative (maximum, minimum, saddle point).
Be able to determine, with the help of the second derivative, whether a function is curved to the left (convex) or curved to the right (concave) in a given interval.
Be able to set up the function equation of polynomial functions from information given in a text, using differential calculus.
Be able to carry out complete curve sketching for the following functions: polynomial functions, rational functions, root functions, trigonometric functions.
Be able to calculate vertical (poles), horizontal, and oblique (slant) asymptotes of rational functions.
Be able to apply polynomial division to determine oblique (slant) asymptotes of rational functions and to find zeros of higher-order polynomials.
Be able to recognize optimization problems and solve them using algebraic and geometric methods.
Be able to identify objectives and objective functions from information given in a text.
Be able to reduce objective functions of two variables with boundary conditions (constraints) to functions of a single variable.
Be able to optimize objective functions using the first derivative.
2. Exam: 12.12.2025
2. Exam: 12.12.2025
Solids of Revolution, Improper Integrals, Lines and Planes in Space
Relevant Exercises (Rhyn):
In the red book: Pages 43 & 44 Exercises 24–26; Pages 45, Exercises 39, 40; Pages 46 & 47, Exercises 48, 49
In the green book: Pages 32, Exercises 14, 15, 17, 18, 22; Page 33, Exercises 23, 24; Page 35, all Exercises; Page 38, Exercise 21; Page 39, Exercise 22; Page 44, Exercises 27–29; Page 51, all Exercises.
Learning Goals:
Be able to compute volumes of revolution using definite integrals (rotation around the x-axis).
Be able to recognize when an integral is improper (infinite limits or singularities) and evaluate it using limits.
Be able to determine whether an improper integral converges or diverges.
Be able to set up the vector equation of a line in space from a support point and a direction vector.
Be able to check whether a given point lies on a line in space.
Be able to determine the positional relationship between two lines in space: intersecting, parallel, or skew.
Be able to compute the vector product of two vectors and apply the area principle correctly.
Be able to represent planes in coordinate form and vector form and convert between these forms.
Be able to solve and geometrically interpret intersection problems between a line and a plane.
Be able to determine the distance from a point to a plane.
Be able to solve geometric problems in three-dimensional space (line and plane positions, distances, intersections, areas) using analytical methods.
Summer-Semester 25/26
3. Exam: 27.03.2026
3. Exam: 27.03.2026
4. Exam: 08.05.2026
4. Exam: 08.05.2026
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